Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the word setting:
“it is finally as though that thing of monstrous interest
were happening in the sky
but the sun is setting and prevents you from seeing it”
—John Ashbery (b. 1927)
“The setting sun is reflected from the windows of the alms-house as brightly as from the rich man’s abode; the snow melts before its door as early in the spring. I do not see but a quiet mind may live as contentedly there, and have as cheering thoughts, as in a palace.”
—Henry David Thoreau (1817–1862)
“When I consider the clouds stretched in stupendous masses across the sky, frowning with darkness or glowing with downy light, or gilded with the rays of the setting sun, like the battlements of a city in the heavens, their grandeur appears thrown away on the meanness of my employment; the drapery is altogether too rich for such poor acting. I am hardly worthy to be a suburban dweller outside those walls.”
—Henry David Thoreau (1817–1862)